# gravitycentrifugal

Implement centrifugal effect of planetary gravity

## Syntax

``````[gx gy gz] = gravitycentrifugal(planet_coordinates)``````
``````[gx gy gz] = gravitycentrifugal(planet_coordinates,model)``````
``````[gx gy gz] = gravitycentrifugal(planet_coordinates,'Custom',value)``````

## Description

### Planetary Gravitational Potential Based on Planetary Rotation Rate

example

``````[gx gy gz] = gravitycentrifugal(planet_coordinates)``` implements the mathematical representation of centrifugal effect for planetary gravity based on planetary rotation rate. This function calculates arrays of `N` gravity values in the x-axis, y-axis, and z-axis of the Planet-Centered Planet-Fixed coordinates for the planet. The function performs these calculations using `planet_coordinates`. You use centrifugal force in rotating or noninertial coordinate systems. Gravity centrifugal effect values are greatest at the equator of a planet.```

### Planetary Gravitational Potential Based on Specified Planetary Model

example

``````[gx gy gz] = gravitycentrifugal(planet_coordinates,model)``` implements the mathematical representation of centrifugal effect based on planetary gravitational potential for the planetary model, `model`.```

### Planetary Gravitational Potential Based on Custom Rotational Rate

example

``````[gx gy gz] = gravitycentrifugal(planet_coordinates,'Custom',value)``` implements the mathematical representation of centrifugal effect based on planetary gravitational potential using the custom rotational rate, `rotational_rate`.```

## Examples

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Calculate the centrifugal effect of Earth gravity in the x-axis at the equator on the surface of Earth.

`gx = gravitycentrifugal([-6378.1363e3 0 0])`
```gx = -0.0339```

Calculate the centrifugal effect of Mars gravity at 15,000 m over the equator and 11,000 m over the North Pole.

```p = [2412.648e3 -2412.648e3 0; 0 0 3376.2e3] [gx, gy, gz] = gravitycentrifugal( p, 'Mars' )```
```p = 2412648 -2412648 0 0 0 3376200 gx = 0.0121 0 gy = -0.0121 0 gz = 0 0```

Calculate the precessing centrifugal effect of gravity for Earth at 15,000 m over the equator and 11,000 m over the North Pole. This example uses a custom planetary model at Julian date 2451545.

```p = [2412.648e3 -2412.648e3 0; 0 0 3376e3]; % Set julian date to January 1, 2000 at noon GMT JD = 2451545; % Calculate precession rate in right ascension in meters pres_RA = 7.086e-12 + 4.3e-15*(JD - 2451545)/36525; % Calculate the rotational rate in a precessing reference % frame Omega = 7.2921151467e-5 + pres_RA; [gx, gy, gz] = gravitycentrifugal(p,'Custom',Omega)```
```gx = 0.0128 0 gy = -0.0128 0 gz = 0 0```

## Input Arguments

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Planet-Centered Planet-Fixed coordinates, specified as an M-by-3 array in meters. The z-axis is positive toward the North Pole. If `model` is `'Earth'`, the planet coordinates are ECEF coordinates.

Data Types: `double`

Planetary model, specified as:

• `'Mercury'`

• `'Venus'`

• `'Earth'`

• `'Moon'`

• `'Mars'`

• `'Jupiter'`

• `'Saturn'`

• `'Uranus'`

• `'Neptune'`

Data Types: `double`

Custom planetary model, specified as a name-value argument, where the value specifies the planetary rotational rate in radians per second.

Example: `'Custom',Omega`

Data Types: `double`

## Output Arguments

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Gravity values in x-axis of the Planet-Centered Planet-Fixed coordinates, returned as an array of M gravity values in meters per second squared (m/s2).

Gravity values in y-axis of the Planet-Centered Planet-Fixed coordinates, returned as an array of M gravity values in meters per second squared (m/s2).

Gravity values in z-axis of the Planet-Centered Planet-Fixed coordinates, returned as an array of M gravity values in meters per second squared (m/s2).

## Version History

Introduced in R2010a